src/HOL/Relation.thy
 author clasohm Mon Feb 05 21:27:16 1996 +0100 (1996-02-05) changeset 1475 7f5a4cd08209 parent 1454 d0266c81a85e child 1695 0f9b9eda2a2c permissions -rw-r--r--
expanded tabs; renamed subtype to typedef;
```     1 (*  Title:      Relation.thy
```
```     2     ID:         \$Id\$
```
```     3     Author:     Riccardo Mattolini, Dip. Sistemi e Informatica
```
```     4         and     Lawrence C Paulson, Cambridge University Computer Laboratory
```
```     5     Copyright   1994 Universita' di Firenze
```
```     6     Copyright   1993  University of Cambridge
```
```     7 *)
```
```     8
```
```     9 Relation = Prod +
```
```    10 consts
```
```    11     id          :: "('a * 'a)set"               (*the identity relation*)
```
```    12     O           :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
```
```    13     trans       :: "('a * 'a)set => bool"       (*transitivity predicate*)
```
```    14     converse    :: "('a * 'b)set => ('b * 'a)set"
```
```    15     "^^"        :: "[('a * 'b) set, 'a set] => 'b set" (infixl 90)
```
```    16     Domain      :: "('a * 'b) set => 'a set"
```
```    17     Range       :: "('a * 'b) set => 'b set"
```
```    18 defs
```
```    19     id_def      "id == {p. ? x. p = (x,x)}"
```
```    20     comp_def    "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
```
```    21     trans_def     "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)"
```
```    22     converse_def  "converse(r) == {(y,x). (x,y):r}"
```
```    23     Domain_def    "Domain(r) == {x. ? y. (x,y):r}"
```
```    24     Range_def     "Range(r) == Domain(converse(r))"
```
```    25     Image_def     "r ^^ s == {y. y:Range(r) &  (? x:s. (x,y):r)}"
```
```    26 end
```